The problem of signal separation is a very broad and fundamental one. A powerful paradigm within which signal separation can be achieved is the assumption that the signals/sources are statistically independent of one another. This is known as Independent Component Analysis (ICA). In this thesis, the theoretical aspects and derivation of ICA are examined, from which disparate approaches to signal separation are drawn together in a unifying framework. This is followed by a review of signal separation techniques based on ICA. Second order statistics based output decorrelation methods are employed to try to solve the challenging problem of separating convolutively mixed signals, in the context of mainly audio source separation and the Cocktail Party Problem. Various optimisation techniques are devised to implement second order signal separation of both artificially mixed signals and real mixtures. A study of the advantages and ...

Magnetic Resonance Imaging (MRI) constitutes a non-invasive medical imaging technique that allows the exploration of the inner anatomy, tissues, and physiological processes of the body. Among the different MRI applications, functional Magnetic Resonance Imaging (fMRI) has slowly become an essential tool for investigating the brain behavior and, nowadays, it plays a fundamental role in clinical and neurophysiological research. Due to its particular nature, specialized signal processing techniques are required in order to analyze the fMRI data properly. Among the various related techniques that have been developed over the years, the General Linear Model (GLM) is one of the most widely used approaches, and it usually appears as a default in many specialized software toolboxes for fMRI. On the other end, Blind Source Separation (BSS) methods constitute the most common alternative to GLM, especially when no prior information regarding the brain ...

Most cognitive processes in the brain are reflected through several aspects simultaneously, allowing us to observe the same process from different biological phenomena. The diverse nature of these biological processes suggests that a better understanding of cerebral activity may be achieved through multimodal measurements. One of the possible multimodal brain recording settings is the combination of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), which is one of the main topics of this thesis. Two groups of EEG-fMRI integration approaches are possible. The first group, commonly called model-based techniques, are very popular due to the fact that the results from such analyses confirm or disprove a specific hypothesis. However, such hypotheses are not always available, requiring a more explorative approach to analyze the data. This exploration is possible with the second group of approaches, the so-called data-driven methods. The data-driven ...

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting a number of mutually independent elements from a set of observed linear mixtures. Motivated by various applications, this work considers a more general and more flexible model: the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups. We argue that this is tantamount to considering multidimensional components, as opposed to the standard ICA case which is restricted to one-dimensional components. In this work, we focus on second-order methods to separate statistically-independent multidimensional components from their linear instantaneous mixture. The purpose of this work is to provide theoretical answers to questions which so far have been discussed mainly in the empirical domain. Namely, we provide a closed-form expression for the figure of merit, the mean square error (MSE), for multidimensional ...

The separation of independent sources from mixed observed data is a fundamental and challenging signal processing problem. In many practical situations, one or more desired signals need to be recovered from the mixtures only. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. The audio signal separation problem is sometimes referred to as The Cocktail Party Problem. When several people in the same room are conversing at the same time, it is remarkable that a person is able to choose to concentrate on one of the speakers and listen to his or her speech flow unimpeded. This ability, usually referred to as the binaural cocktail party effect, results in part from binaural (two-eared) hearing. In contrast, ...

This thesis concentrates on a major problem within audio signal processing, the separation of source signals from musical mixtures when only a single mixture channel is available. Source separation is the process by which signals that correspond to distinct sources are identified in a signal mixture and extracted from it. Producing multiple entities from a single one is an extremely underdetermined task, so additional prior information can assist in setting appropriate constraints on the solution set. The approach proposed uses prior information such that: (1) it can potentially be applied successfully to a large variety of musical mixtures, and (2) it requires minimal user intervention and no prior learning/training procedures (i.e., it is an unsupervised process). This system can be useful for applications such as remixing, creative effects, restoration and for archiving musical material for internet delivery, amongst others. Here, ...

Epilepsy is a neurological condition that manifests in epileptic seizures as a result of an abnormal, synchronous activity of a large group of neurons. Depending on the affected brain regions, seizures produce various severe clinical symptoms. Epilepsy cannot be cured and in many cases is not controlled by medication either. Surgical resection of the region responsible for generating the epileptic seizures might offer remedy for these patients. Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measure the changes of brain activity in time over different locations of the brain. As such, they provide valuable information on the nature, the timing and the spatial origin of the epileptic activity. Unfortunately, both techniques record activity of different brain and artefact sources as well. Hence, EEG and fMRI signals are characterised by low signal to noise ratio. Data quality and the vast amount ...

This thesis is concerned with three closely related problems. The first one is called Multiple-Input Multiple-Output (MIMO) Instantaneous Blind Identification, which we denote by MIBI. In this problem a number of mutually statistically independent source signals are mixed by a MIMO instantaneous mixing system and only the mixed signals are observed, i.e. both the mixing system and the original sources are unknown or ‘blind’. The goal of MIBI is to identify the MIMO system from the observed mixtures of the source signals only. The second problem is called Instantaneous Blind Signal Separation (IBSS) and deals with recovering mutually statistically independent source signals from their observed instantaneous mixtures only. The observation model and assumptions on the signals and mixing system are the same as those of MIBI. However, the main purpose of IBSS is the estimation of the source signals, whereas ...

This thesis is concerned with three closely related problems. The first one is called Multiple-Input Multiple-Output (MIMO) Instantaneous Blind Identification, which we denote by MIBI. In this problem a number of mutually statistically independent source signals are mixed by a MIMO instantaneous mixing system and only the mixed signals are observed, i.e. both the mixing system and the original sources are unknown or ¡blind¢. The goal of MIBI is to identify the MIMO system from the observed mixtures of the source signals only. The second problem is called Instantaneous Blind Signal Separation (IBSS) and deals with recovering mutually statistically independent source signals from their observed instantaneous mixtures only. The observation model and assumptions on the signals and mixing system are the same as those of MIBI. However, the main purpose of IBSS is the estimation of the source signals, whereas ...

Reverberation is the sum of reflected sound waves and is present in any conventional room. Speech communication devices such as mobile phones in hands-free mode, tablets, smart TVs, teleconferencing systems, hearing aids, voice-controlled systems, etc. use one or more microphones to pick up the desired speech signals. When the microphones are not in the proximity of the desired source, strong reverberation and noise can degrade the signal quality at the microphones and can impair the intelligibility and the performance of automatic speech recognizers. Therefore, it is a highly demanded task to process the microphone signals such that reverberation and noise are reduced. The process of reducing or removing reverberation from recorded signals is called dereverberation. As dereverberation is usually a completely blind problem, where the only available information are the microphone signals, and as the acoustic scenario can be non-stationary, ...

The brain is the most important signal processing unit in the human body. It is responsible for receiving, processing and storing information. One of the possibilities to study brain functioning is by placing electrodes on the scalp and recording the synchronous neuronal activity of the brain. Such a recording measures a combination of active processes in the whole brain. Unfortunately, it is also contaminated by artifacts. By extracting the artifacts and removing them, cleaned recordings can be investigated. Furthermore, it is easier to look at specific brain activities, like an epileptic seizure, than at a combination. In this thesis, we present different mathematical techniques that can be used to extract individual contributing sources from the measured signals for this purpose. We focused on Canonical Correlation Analysis (CCA), Independent Component Analysis (ICA) and Canonical/ Parallel Factor Analysis (CPA). We show that ...

In this thesis, a general solution to the component separation problem in images is introduced. Unlike most existing works, the spatial dependencies of images are modelled in the separation process with the use of Markov random fields (MRFs). In the MRFs model, Cauchy density is used for the gradient images. We provide a general Bayesian framework for the estimation of the parameters of this model. Due to the intractability of the problem we resort to numerical solutions for the joint maximization of the a posteriori distribution of the sources, the mixing matrix and the noise variances. For numerical solution, four different methods are proposed. In first method, the difficulty of working analytically with general Gibbs distributions of MRF is overcome by using an approximate density. In this approach, the Gibbs distribution is modelled by the product of directional Gaussians. The ...

In modern devices which provide hands-free speech capturing functionality, such as hands-free communication kits and voice-controlled devices, the received speech signal at the microphones is corrupted by background noise, interfering speech signals, and room reverberation. In many practical situations, the microphones are not necessarily located near the desired source, and hence, the ratio of the desired speech power to the power of the background noise, the interfering speech, and the reverberation at the microphones can be very low, often around or even below 0 dB. In such situations, the comfort of human-to-human communication, as well as the accuracy of automatic speech recognisers for voice-controlled applications can be signi cantly degraded. Therefore, e ffective speech enhancement algorithms are required to process the microphone signals before transmitting them to the far-end side for communication, or before feeding them into a speech recognition ...

Music is built from sound, ultimately resulting from an elaborate interaction between the sound-generating properties of physical objects (i.e. music instruments) and the sound perception abilities of the human auditory system. Humans, even without any kind of formal music training, are typically able to ex- tract, almost unconsciously, a great amount of relevant information from a musical signal. Features such as the beat of a musical piece, the main melody of a complex musical ar- rangement, the sound sources and events occurring in a complex musical mixture, the song structure (e.g. verse, chorus, bridge) and the musical genre of a piece, are just some examples of the level of knowledge that a naive listener is commonly able to extract just from listening to a musical piece. In order to do so, the human auditory system uses a variety of cues ...

In numerous signal processing applications one disposes of multiple probes, delivering simultaneously information about one or multiple observed processes. The resulting multidimensional time series are often highly redundant and may contain stochastic contributions. The perception of the useful information becomes therefore very difficult and sometimes impossible. Thus, the major issue of concern of this thesis resides in the development of novel algorithms for the extraction of the salient and characteristic features of multidimensional time series. The proposed algorithms are based on parametric signal processing, namely we assume that the features of the experimental data can be represented efficiently by a specific model. We present a global framework for the selection of a specific model out of the large span of techniques proposed in the literature. For the selection of the model classes we use, in addition to prior knowledge about ...